Group data based on intervals and assign group to new column

You may use cut and create groups based on defined intervals.

transform(DF, GROUP = cut(AGE, c(0, seq(19, max(AGE) + 10, 10)), labels = FALSE))

#    NAME AGE GROUP
#1   Gait  33     3
#2    Roc  43     4
#3     Bo  37     3
#4  Hernd  45     4
#5    Bet  44     4
#6    Oln  35     3
#7    Gai  22     2
#8   Rock  30     3
#9    Mil  38     3
#10  Arli  23     2
#11    Re  45     4
#12  Fred  43     4
#13    Ro  67     6
#14  Rock  43     4
#15 Wheat  28     2
#16 Germa  47     4
#17  Rock  16     1
#18  Nort  29     2
#19  Arli  22     2
#20 Rockv  31     3

The key part here is how we create intervals with c and seq which define the groups.

c(0, seq(19, max(DF$AGE) + 10, 10))
#[1]  0 19 29 39 49 59 69